“Computer Chess” is a conscious artifact, an experience akin to cracking open an ancient Altair 8800 to peer at the tiny people inside. Set over the course of three days at an anonymous hotel sometime around the dawn of the 1980s, the film follows a motley group of computer wonks as they pit chess-playing algorithms against each other; the winning program will try to beat the event’s host, a fatuous chess nerd (delightfully played by Boston film critic and teacher Gerald Peary) who has yet to lose to a machine.

Writer-director Andrew Bujalski — the Boston-born filmmaker (“Funny Ha Ha,” “Mutual Appreciation”) who helped make the world safe for mumblecore in the early 2000s — has thus set his movie at a critical juncture in modern history: the moment just before computers became personal, when intelligence and artificial intelligence danced nervously around each other, uncertain as to who was leading. Rather than make a grand statement, Bujalski gets in close and shoots for the wayward poetry of connection — human, electronic, erotic. What his characters are too obsessed or distracted to see, he hopes we will.

That muzziness extends to the visual style, which at times comes close to suffocating “Computer Chess” in the crib. Bujalski has shot his film on period video equipment, resulting in a boxy, blurry, B&W look that really does feel like outtakes unearthed from an early-Reagan-era seminar. It’s a formally audacious move that, taken with the film’s general plotlessness and socially inept characters, narrows the potential audience. Their loss. “Computer Chess” is deeply strange and occasionally impenetrable, yet it’s also surreally funny, with touches of science fiction that bedevil the proceedings with outré possibilities.

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More critically, the movie’s prophetic about where we are in 2013. Uncertain of how to behave when they’re face to face, the characters fumble toward the safety of mediated relationships. “You know what the future of computers is?” asks one attendee. “Dating.” It only seems like fantasy at the time.

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Individual portraits rise out of this primordial analog stew: a nervous Allied Labs technician named Les Carbray (James Curry), hoping his crate full of wires is smarter than all the other crates full of wires. A sad-looking psychologist named Beuscher, played by Wiley Wiggins, once the kid of “Dazed and Confused” and now unrecognizably middle-aged. A vaguely threatening interloper (Jim Miller) who may be scouting for the Department of Defense. Shelly (Robin Schwartz), the lone woman programmer and thus a novelty on the order of a two-headed horse. The married professor (Gordon Kindlmann) with his wife (Anne Dodge) and baby — as much an alien in these surroundings as Shelly.

Two characters stick out. Papageorge (Myles Paige) is an egotistical programmer who hopes to crash the event and ends up annoying everyone — he’s Steve Jobs without the personal charm. His opposite number is Peter (Patrick Riester), a young tech on the TSAR team and a pathologically shy beanpole who begins to wonder if the computers aren’t hosting a quiet revolution of their own.

It’s Peter who has the most comic run-ins with the other group using the hotel’s conference suites: a touchy-feely gang of New Age seekers headed by an African self-help guru. In the queasy highlight of “Computer Chess,” two of them (Chris Doubek and Cyndi Williams) trap Peter in their hotel room for a hoped-for bout of swinging. They don’t even speak the same language. Where the couple sees the boy’s life as limited by the 64 squares of a chessboard, he sees the number of potential moves: 10 to the 120th power. And yet both sides are desperate to touch something larger than themselves. Even the computers in this movie are lonely.

In its extremely minimalist fashion, “Computer Chess” is about the digital apocalypse waiting around the corner for these characters — waiting for us all. Off-kilter omens abound: an elevator full of cats, a spooky woman who haunts the lobby, split-screens and sudden shifts to color or photographic negative. The ground is tilting away from the humans. “By 1986,” says one of the wonks darkly, “you won’t stand a chance.”